🧪 Elements
22 lessons

Gases & the Ideal Gas Law

A gas is chaos with rules. Four knobs — pressure, volume, temperature, amount — locked together by one equation.

lesson 2 of 3 in this unit

Builds on: 3.1 Solid, Liquid, Gas2.2 The Mole: Chemistry's Dozen

Pressure is drumming

A gas particle hits the container wall and bounces off, giving the wall a tiny shove. Multiply by 10²³ collisions per second and the drumming blurs into a steady push: pressure. This picture makes gas behaviour almost obvious. Shrink the volume → particles hit walls more often → pressure rises. Heat the gas → particles hit harder and more often → pressure rises. Add more gas → more drummers → pressure rises.

One law to rule the knobs

P V = n R Tpressure × volume = moles × gas constant × absolute temperature (in kelvin!)

Everything above is packed into this one line, with R ≈ 8.314 J/(mol·K) as the conversion constant. The non-negotiable detail: T must be in kelvin (K = °C + 273.15). Celsius has its zero at an arbitrary point — water’s freezing — while gas physics cares about absolute motion. At 0 K motion stops; doubling kelvin genuinely doubles the pressure. Doubling “degrees Celsius” means nothing.

A famous consequence: at room conditions, one mole of any ideal gas fills about 24 litres — hydrogen, oxygen, CO₂ alike. The identity of the particles barely matters when they spend their lives far apart.

Special cases you already know

  • Squeeze at constant T (Boyle): halve V → double P. Syringes, pistons, diving.
  • Heat at constant V (Gay-Lussac): P rises with T. Why aerosol cans say “never throw into fire”.
  • Heat at constant P (Charles): V grows with T. Why a hot-air balloon rises and a sealed bag puffs up in the sun.
“Ideal”?

The law assumes point-particles with no attractions — nearly true for ordinary gases at ordinary conditions. Squeeze hard or cool near condensation and the intermolecular forces from the last lesson reappear; that’s exactly when real gases start to liquefy and the law bends.

⚗️ LabThe Piston Machine

A gas in a cylinder with three knobs and one pressure gauge.

  • Halve the volume at fixed T — watch P double as the wall-drumming doubles.
  • Heat from 300 K to 600 K at fixed volume: the particles blush red and P doubles.
  • Find settings where the gauge reads ≈ 101 kPa — that’s the air around you.
1.0 mol
300 K
25 L

Work it by hand — 0 / 4

No multiple choice here: compute the value and type it. Suffixes like 2.5k, 20m or 100µ are understood; answers within ±2% count.

1. What pressure (kPa) does 1 mol of gas exert in 10 L at 300 K? (R = 8.314)
2. A balloon holds 24 L at 300 K. You heat it to 350 K at constant pressure. New volume?
3. Convert 25 °C to kelvin.
4. A sealed 2 L bottle at 100 kPa is squeezed to 0.8 L at constant temperature. New pressure?

Check your understanding

1. What is gas pressure, microscopically?

2. Why must T be in kelvin in PV = nRT?

3. You squeeze a syringe (sealed, constant temperature) to half its volume. The pressure…

4. Why do aerosol cans warn against fire?